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Question

A physical quantity is given by X=[MaLbTc]. The percentage error in measurement of M,L and T are α,β and γ respectively. Then, the maximum % error in the quantity X is:

A
aα+bβ+cγ
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B
aα+bβcγ
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C
aα+bβ+cγ
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D
None of these
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Solution

The correct option is A aα+bβ+cγ
The quantity is given as X=[MaLbTc]
Taking logrithm on both sides lnX=alnM+blnL+clnT
Differentiating and multiplying by 100, we get
ΔXX×100=aΔMM×100 +bΔLL×100+cΔTT×100 ........(1)

Given: ΔMM×100=α ΔLL×100=β ΔTT×100=γ
Thus % error in X, ΔXX×100=aα+bβ+cγ

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